The function `x = A sin^2 (omega)t + B cos^2 (omega)t + Csin (omega)t cos (omega)t` represent (SHM) for which of the option(s).

Options

A. For all value of `A,B and C` (except C = 0)
B. `A = -B, C = 2 B, amplitude = |B sqrt(2)|`
C. `A = B, C = 0`
D. `A = B, C = 2 B, amplitude = |B|`

Answer

B, D

Explanation

For `A = -B` and `C = 2B`
`X = B cos 2 omega t + B sin 2 omega t = sqrt(2) B sin [2 omega t+(pi)/(4)]`
This is equation of `SHM` of amplitude `sqrt(2) B`.
If `A =B` and `C=B`, then `X =B + B sin 2 omega t`
This is also equation of `SHM` about the point `X = B`. Function oscillates between `X = 0` and `X = 2B` with amplitude `B`.